Solve the system y = -x + 7 and y = 0.5(x - 3)2

explain the answer

x=5, x=-1

Step-by-step explanation:

Since both equations are equal to y, we can set them equal to each other

y = -x + 7 and y = 0.5(x - 3)2

-x + 7 = 0.5(x - 3)^2

Distribute the right hand side by Foiling

-x+7 =.5 ( x^2 -3x-3x+9)

Combine like terms

-x+7 = .5( x^2 -6x+9)

Distribute the .5

-x+7 = .5x^2 -3x+4.5

Add x to each side

-x+x+7 = .5x^2 -3x+x+4.5

7 =  .5x^2 -2x+4.5

Subtract 7 from each side

7 -7= .5x^2 -2x+4.5-7

0 = .5x^2 -2x-2.5

Multiply by 2 to clear the decimals

0 = x^2 -4x -5

Factor

0 = (x-5) (x+1)

Using the zero product property

x-5=0  x+1 =0

x=5, x=-1